In this paper we propose a simple naive estimator of the failure rate function. This estimate is asymptotically unbiased but not consistent. It can be smoothed by using any band limited window. We show that this smoothed estimate is equivalent to estimates obtainable from the modified sample hazard function, as in Rice and Rosenblatt (1976). We obtain the asymptotic distribution of the global deviation of the smoothed estimate from the failure rate function, which can then be used to construct uniform confidence bands. We illustrate the rate of convergence of our estimator by a Monte-Carlo simulation.

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